Add broth to the pot gradually, whisking well to work out any lumps. Bring soup to a simmer and cook until flavorful and thickened, about 45 minutes. Stir frequently and skim as needed.

Meanwhile, bring a large pot of water to boil. Have ready a large bowl of ice water. Add reserved asparagus florets and parboil, cooking until just tender, 3-4 minutes. Remove florets with a slotted spoon and plunge them into ice water. Once cool, drain and reserve.

Strain soup, reserving both the solids and the broth. Purée the solids, adding broth as needed to facilitate puréeing. Combine purée with enough of the reserved broth to achieve the consistency of heavy cream. Strain the soup through a fine-mesh sieve, if desired. Return the soup to a simmer.

Remove soup from heat and add cream and lemon juice. Taste and season with salt and pepper. Garnish with the reserved tips.